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Overview and Comparison of Feedback-Based Dynamic Beam Focusing Techniques for Long-Range Wireless Power Transfer

Electronics 2025, 14(11), 2155; https://doi.org/10.3390/electronics14112155

by Charleston Dale Ambatali

Reviewer 1:

Bing Xue

Reviewer 2: Anonymous

Reviewer 3: Anonymous

Reviewer 4:

Shu-Hung Lee

Electronics 2025, 14(11), 2155; https://doi.org/10.3390/electronics14112155

Submission received: 15 February 2025 / Revised: 27 March 2025 / Accepted: 1 April 2025 / Published: 26 May 2025

(This article belongs to the Special Issue New Insights of Wireless Power Transfer)

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper reviews different methods for beamforming techniques. Thanks for your clear review.

I have some questions:

1) The title includes 'review'. If I understood correctly, this is a research article.? or review paper? So, I suggest the author pay more attention to the title. New knowledge is limited.

2) line 84 is not clear. Which is the 'Rayleigh coefficient'? Please explain eq. (2) and (3) before 'The maxima of this is...'

3) What kind of blockage do you use for the third simulation case?

4) whether the antennas are in their far-field region in all the simulations? It seems they are too close in the figures. In the practical environment, they are far away from each other. And what you focus on is also the long range. From my understanding, your simulation should be implemented with a least 1-2 meter distance. The near-field region can meet the far-field assumption. The coupling between antennas is complex. If your simulation cannot meet the far field, please re-run the simulations. The mixed simulation method can be used, like FEM for element simulation and MoM for long-range simulation. It can help you to save time and make the simulation achievable.

5) For the number of iterations comparisons, I do not suggest the author compare the number of iterations since the convergence conditions will affect the number. And the iteration number cannot show the complexity of the algorithms. I do not say Fig.3 is not useful. It is still useful. I suggest the author compare the implementation time + the number of iterations. Surely the time is also not a good measure to show the performance of the algorithms. However, it can be somehow useful.

6) I suggest the author makes a large table to show the advantages and disadvantages of all the methods.

Comments on the Quality of English Language

The sentences are correct. But, some explanations are not clear. I suggest the author carefully proofread the paper.

Author Response

Dear Reviewer,

I appreciate the time and effort that you have dedicated to provide feedback on my manuscript entitled “Overview and Comparison of Feedback-based Dynamic Beam Focusing Techniques for Long-Ranged Wireless Power Transfer". The comments are very helpful and they have provided valuable insights on how we can refine the content and style of our manuscript. We have carefully incorporated all comments in this revision. The detailed responses to each of the comments can be found after this cover statement.

I have also provided both a clean version and a version with changes highlighted in blue with a list of all changes summarized in the first page. I greatly appreciate the significant improvements that have resulted from your feedback.

I hope that you find my revised manuscript suitable for publication as a research article in the MDPI Electronics Special Issue: New Insights of Wireless Power Transfer. I look forward to hearing from you.

Sincerely,
Charleston Dale M. Ambatali

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Comment 1: The title includes 'review'. If I understood correctly, this is a research article.? or review paper? So, I suggest the author pay more attention to the title. New knowledge is limited.

Response 1: Thank you for this comment and I apologize for the confusion. It should be "Overview and Comparison..." instead of "Review and Comparison...", in which the article generates new data comparing the different methods in simulation. This has been reflected in the new version.

Comment 2: line 84 is not clear. Which is the 'Rayleigh coefficient'? Please explain eq. (2) and (3) before 'The maxima of this is...'

Response 2: I apologize for the lack of clarity in the writing of this subsection. Equation (2) is the Rayleigh quotient (not coefficient), and its maximum value is the maximum eigenvalue of the matrix in between the vectors in the numerator. This is expressed explicitly by Equation (3). Moreover, Equation (2) gives us insight on the maximum possible WPT efficiency as restricted by the environmental conditions through the S-parameters. Furthermore, it also provides the insight that maximum efficiency is achievable by finding the eigenvector corresponding to the maximum eigenvalue. This eigenvector can then be used to configure the phase and amplitude of each element of the transmit array subjected to a maximum power output constraint.

Comment 3: What kind of blockage do you use for the third simulation case?

Response 3: Thank you for this inquiry. For cases 1 and 3, perfect electric conductors were used as obstructions. The revised version provides more descriptions about the setup of each electromagnetic simulation cases.

Comment 4: Whether the antennas are in their far-field region in all the simulations? It seems they are too close in the figures. In the practical environment, they are far away from each other. And what you focus on is also the long range. From my understanding, your simulation should be implemented with a least 1-2 meter distance. The near-field region can meet the far-field assumption. The coupling between antennas is complex. If your simulation cannot meet the far field, please re-run the simulations. The mixed simulation method can be used, like FEM for element simulation and MoM for long-range simulation. It can help you to save time and make the simulation achievable.

Response 4: Thank you for this insightful comment. I have added a "Scope and delimitations" section to address this issue. I do agree that this work will benefit with an increased distance between antennas, however, due to the time constraints, I have elected to defend the current design of my simulation. Long-distance WPT is not envisioned to operate in the far-field zone of EM propagation due to low WPTE, rather, it will be operated in the radiative near-field zone. The boundary between these zones is equal to 2D²/λ (also called the Fraunhofer distance) where D is the maximum antenna length and λ is the operating wavelength. Since this boundary scales quadratically, a sufficient practical antenna size can enable transmission to kilometer distances. In my simulation design, the antenna size is only enough to have Fraunhofer distances of less than 1 meter. However, since all of them operate in the radiative near-field zone, they can be interpreted as an equivalent scaled version of the envisioned practical implementation. Moreover, I designed the simulation to focus more on comparing the convergence time and steady-state efficiency, and less on the practical aspect of it to save computer memory and time. I am grateful for your suggestion and I can incorporate it in a future work to simulate the gigascale antenna implementation for space-based solar power which I am working on at the moment. Thank you again for this comment.

Comment 5: For the number of iterations comparisons, I do not suggest the author compare the number of iterations since the convergence conditions will affect the number. And the iteration number cannot show the complexity of the algorithms. I do not say Fig.3 is not useful. It is still useful. I suggest the author compare the implementation time + the number of iterations. Surely the time is also not a good measure to show the performance of the algorithms. However, it can be somehow useful.

Response 5: Thank you for this feedback. I have incorporated the processing time that my code takes to run each iteration into the comparison, except for the both-sides retrodirective array which uses purely analog circuitry which can be assumed to run much faster compared to the round-trip propagation time. Added more discussion on how each of them were calculated.

Comment 6: I suggest the author makes a large table to show the advantages and disadvantages of all the methods.

Response 6: Thank you for this comment. I have added a table summarizing the discussion in Section 3.

------------------------------------------------------

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript shows a good overview of wireless power transfer. However, the numerical results are for cases that are unrealistic in practical cases where the system size is much larger. In more practical cases, the simulation times will be extraordinarily high, and the simulation results will be substantially different. In fact, much of the simulation results are in the near-field region and may not be applicable in real situations.

Author Response

Dear Reviewer,

Sincerely,
Charleston Dale M. Ambatali

------------------------------------------------------

Comment 1: The manuscript shows a good overview of wireless power transfer. However, the numerical results are for cases that are unrealistic in practical cases where the system size is much larger. In more practical cases, the simulation times will be extraordinarily high, and the simulation results will be substantially different. In fact, much of the simulation results are in the near-field region and may not be applicable in real situations.

Response 1: Thank you for your kind feedback. I would like to respectfully contend on the comment that the near-field region is not an applicable case in practical situations. From [Ref1] and [Ref2], long-range wireless power transfer is envisioned to operate in the radiative near-field zone, which is the region of propagation between the reactive near-field (capacitive and inductive), and the far-field (plane wave propagation). The maximum distance of this region is quadratically proportional to the maximum antenna length, and gigascale antennas were conceptualized from this idea to enable power transmission from space to ground. I designed the electromagnetic simulations to be a scaled version of the envisioned practical implementations as all of them operate in the radiative near-field. Moreover, I designed them with more focus on demonstrating the convergence time and steady-state efficiency of the different methods, and less on the practical aspects. This discussion has been added to a new "Scope and delimitations" section. Thank you again for your valuable feedback.

[Ref1] V. R. Gowda, O. Yurduseven, G. Lipworth, T. Zupan, M. S. Reynolds, and D. R. Smith, “Wireless power transfer in the radiative near field,” IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 1865–1868, 2016.
[Ref2] D. R. Smith, V. R. Gowda, O. Yurduseven, S. Larouche, G. Lipworth, Y. Urzhumov, and M. S. Reynolds, "An analysis of beamed wireless power transfer in the Fresnel zone using a dynamic, metasurface aperture," Journal of Applied Physics, vol. 121 no. 1, 2017.

Reviewer 3 Report

Comments and Suggestions for Authors

1. The paper presents various dynamic beam focusing techniques but lacks a detailed prototype characterization to validate the proposed methods. How can the presented approaches be effectively validated in a real-world setup, and how do you plan to address the absence of experimental validation in future work?

2. The paper provides mathematical formulations and simulations but lacks an in-depth theoretical analysis of the underlying principles governing the feedback-based beam focusing methods. Could you expand on the theoretical models or assumptions that support the claimed efficiencies and convergence times?

3. The paper relies heavily on simulations using fixed parameters, such as in MATLAB and Ansys HFSS, for performance evaluation. How do you ensure that these simulation results will accurately reflect real-world performance, especially considering potential real-world interference or dynamic conditions not fully captured in your models?

4. The paper compares methods based on convergence time and steady-state efficiency but does not discuss the trade-offs between these factors in detail. How would you balance the speed of convergence with the achievable efficiency in real-time systems, particularly for long-range wireless power transfer?

5. While the paper suggests that feedback-based dynamic beam focusing methods are scalable, it does not provide detailed analyses on how these techniques might scale in large systems. What challenges do you anticipate when scaling up these systems to gigascale antenna arrays, and how might the increased system complexity impact both performance and implementation?

Comments on the Quality of English Language

The English language of the manuscript is fairly poor.

Author Response

Dear Reviewer,

Sincerely,
Charleston Dale M. Ambatali

------------------------------------------------------

Comment 1: The paper presents various dynamic beam focusing techniques but lacks a detailed prototype characterization to validate the proposed methods. How can the presented approaches be effectively validated in a real-world setup, and how do you plan to address the absence of experimental validation in future work?

Response 1: Thank you for this inquiry. I have added more details in the recommendation section to address this. A hardware implementation of the different algorithms using SDRs and recreating the experiment setup in [Ref1] is an option for future work to validate the comparison performed in this submission. [Ref1] C. D. M. Ambatali, S. Nakasuka, B. Yang, N. Shinohara, "Analysis and experimental validation of the WPT efficiency of the both-sides retrodirective system," Space Solar Power and Wireless Transmission, vol. 1 pp. 48-60, 2024.

Comment 2: The paper provides mathematical formulations and simulations but lacks an in-depth theoretical analysis of the underlying principles governing the feedback-based beam focusing methods. Could you expand on the theoretical models or assumptions that support the claimed efficiencies and convergence times?

Response 2: Thank you for this comment. I have expanded Section 3 and added a diagram to illustrate the operation of feedback-based methods. The theory behind the calculation of the efficiency can be found in Section 2.3, specifically Equation (2) which uses the S-parameters of the system. This was generalized in [Ref2], but it has been interpreted as channel state information in various works predating [Ref2]. These parameters describe the scattering of electromagnetic waves in a circuit, but it has been used to model scattering of waves in a wireless environment. From the S-parameters, the efficiency can be solved using the eigenvectors associated with the channel conditions as expressed by Equation (5). A more detailed discussion about how the convergence time is computed is added to the text. It has also been expanded. In the previous submission, the convergence time was assumed to be synonymous to the amount of round trip times it takes for the system to find a steady-state. In this version, we also added the computational complexity of each method. Finally, a more detailed discussion was also added for the electromagnetic simulation setups from which the S-parameters are calculated and then the theoretical maximum WPTE can be computed using Equation (2) and (3). [Ref2] Q. Yuan, "S-Parameters for Calculating the Maximum Efficiency of a MIMO-WPT System: Applicable to Near/Far Field Coupling, Capacitive/Magnetic Coupling," IEEE Microwave Magazine, vol. 24 pp. 40-48, 2023.

Comment 3: The paper relies heavily on simulations using fixed parameters, such as in MATLAB and Ansys HFSS, for performance evaluation. How do you ensure that these simulation results will accurately reflect real-world performance, especially considering potential real-world interference or dynamic conditions not fully captured in your models?

Response 3: Thank you for your feedback. In this comparison, we wanted only to focus on comparing the different methods in static conditions to show how fast they converge and if they achieve a steady-state efficiency close to the theoretical maximum. We plan to do a dynamic simulation to compare them again, but a framework to do such a simulation has been done in another work we submitted to another journal whose preprint is available here, but only applied to the both-sides retrodirective antenna. We recommend to do the same setup in a future work, but for this submission, I only wanted to focus on the comparison between different methods under different conditions.

Comment 4: The paper compares methods based on convergence time and steady-state efficiency but does not discuss the trade-offs between these factors in detail. How would you balance the speed of convergence with the achievable efficiency in real-time systems, particularly for long-range wireless power transfer?

Response 4: Thank you for this inquiry. More discussion in the text is added to address this. As mentioned in the results, there is a trade-off between complexity, convergence time, and steady-state efficiency. Although, this work did not present any theoretical analysis to prove this, the results observed assert the claim. To balance them depends on the resources of the implementation and on how fast the system changes over time.

Comment 5: While the paper suggests that feedback-based dynamic beam focusing methods are scalable, it does not provide detailed analyses on how these techniques might scale in large systems. What challenges do you anticipate when scaling up these systems to gigascale antenna arrays, and how might the increased system complexity impact both performance and implementation?

Response 5: Thank you for this comment. I removed the statement about scalability of the different methods as no appropriate analysis framework can be designed to prove the claims. The challenge of scalability is currently on the ability of the method to be modularized so partial implementation is possible. This is added in the recommendation for future work.

Reviewer 4 Report

Comments and Suggestions for Authors

This paper reviews various existing feedback-based long-range wireless power transfer (WPT) techniques and evaluates their convergence speed, implementation complexity, and steady-state efficiency through simulation analysis. The results indicate that methods based on channel state information (CSI) measurement and the bidirectional retrodirective system can achieve high-efficiency power transfer in a shorter time, albeit with increased implementation complexity.

There are some issues in this paper that need to be supplemented and improved, as described below.

1.In line 28, the abbreviation 'WPTE' is introduced. It is recommended to include its full form, 'Wireless Power Transfer Efficiency,' to ensure clarity for readers.

2.In the caption of Figure 2, the phrase 'A 2 × 2 transmitter array sending power to two (2) 2 × 2 receiver arrays' should be revised by removing '(2)' to avoid potential confusion for readers.

3.In line 82, the text describes the formula for the Wireless Power Transfer Efficiency (WPTE) as the ratio of the power at the receiver (derived from v1b = S21Tv2f) to the input power at the generator (from v2f), and it claims that this relationship is shown in Figure 2. However, Figure 2 does not depict this relationship.

4.In the manuscript, Figure 4 and Figure 5, mentioned in lines 92 and 95, are missing.

5.In line 106, ‘Feedback can be in the form of telemetry data sent from the receiver to the transmitter in conjunction with optimization techniques maximizing the received power computed using 6.’ To improve readability, it is recommended to replace ‘using 6’ with ‘using Equation (6).

6.In line 160, 'p = {pk}' is written, where pk is just a single value. How does it become a vector? This notation for defining the vector is likely to cause confusion among readers.

7.In line 154, ‘v2f(k) is the kth pilot signal,’ while in line 192, ‘v2f(k) is the transmit signal after k iterations.’ Please provide a detailed explanation of the similarities and differences between these two definitions.

8.Please include a table in Section 3.4 that compares the various methods in terms of complexity, convergence time, and efficiency, along with their advantages and disadvantages.

9.In line 234, 'For DRIS, the Nelder-Mead method [24] with a convergence condition of 0.01, reflection coefficient α = 1, reflection coefficient γ = 4, contraction coefficient ρ = 0.5, and shrinkage coefficient σ = 0.5 is used.' Here, both α and γ are referred to as reflection coefficients. What is the difference between them? What is the function of the shrinkage coefficient σ = 0.5? Additionally, 'coefficienct' is a typo.

10.In line 265, 'the CSI estimation using LSE and both-sides retrodirective system boasts the least convergence time needed to achieve the maximum possible WPT efficiency, but their implementation is more complex compared to the iterative methods.' Why is the implementation of CSI estimation using LSE and the both-sides retrodirective system more complex? This should be further elaborated.

Comments on the Quality of English Language

Please refer to the comments and suggestions for authors.

Author Response

Dear Reviewer,

Sincerely,
Charleston Dale M. Ambatali

------------------------------------------------------

Comment 1: In line 28, the abbreviation 'WPTE' is introduced. It is recommended to include its full form, 'Wireless Power Transfer Efficiency,' to ensure clarity for readers.

Response 1: Thank you for this comment. The text has been revised.

Comment 2: In the caption of Figure 2, the phrase 'A 2 × 2 transmitter array sending power to two (2) 2 × 2 receiver arrays' should be revised by removing '(2)' to avoid potential confusion for readers.

Response 2: Thank you for this comment. The text has been revised. The figure has also been separated to three different figures for better clarity.

Comment 3: In line 82, the text describes the formula for the Wireless Power Transfer Efficiency (WPTE) as the ratio of the power at the receiver (derived from v1b = S21Tv2f) to the input power at the generator (from v2f), and it claims that this relationship is shown in Figure 2. However, Figure 2 does not depict this relationship.

Response 3: I apologize for this confusion. This references Equation (2) and not Figure 2. I have revised the manuscript code to make sure this mistake did not carry over in the next revision.

Comment 4: In the manuscript, Figure 4 and Figure 5, mentioned in lines 92 and 95, are missing.

Response 4: I apologize for this confusion. Similar to comment 3, This references Equations (4) and (5). I have revised the manuscript code to make sure this mistake did not carry over in the next revision.

Comment 5: In line 106, ‘Feedback can be in the form of telemetry data sent from the receiver to the transmitter in conjunction with optimization techniques maximizing the received power computed using 6.’ To improve readability, it is recommended to replace ‘using 6’ with ‘using Equation (6).

Response 5: Thank you for this comment. Similar to comment 3, This references Equations (4) and (5). I have revised the manuscript code to make sure this mistake did not carry over in the next revision.

Comment 6: In line 160, 'p = {pk}' is written, where pk is just a single value. How does it become a vector? This notation for defining the vector is likely to cause confusion among readers.

Response 6: Thank you for this feedback. The text has been revised for better clarity.

Comment 7: In line 154, ‘v2f(k) is the kth pilot signal,’ while in line 192, ‘v2f(k) is the transmit signal after k iterations.’ Please provide a detailed explanation of the similarities and differences between these two definitions.

Response 7: I apologize for this confusion. They are the same quantity, both of them are transmit signals which provide power from the transmitter to the receiver indexed by (k). For every new iteration is a new index value.

Comment 8: Please include a table in Section 3.4 that compares the various methods in terms of complexity, convergence time, and efficiency, along with their advantages and disadvantages.

Response 8: Thank you for this valuable comment. A table summarizing the comparisons between each method has been added.

Comment 9: In line 234, 'For DRIS, the Nelder-Mead method [24] with a convergence condition of 0.01, reflection coefficient α = 1, reflection coefficient γ = 4, contraction coefficient ρ = 0.5, and shrinkage coefficient σ = 0.5 is used.' Here, both α and γ are referred to as reflection coefficients. What is the difference between them? What is the function of the shrinkage coefficient σ = 0.5? Additionally, 'coefficienct' is a typo.

Response 9: I apologize again for the confusion. The reflection coefficient is α and the contraction coefficient is γ. Typographical errors have also been thoroughly checked. Thank you.

Comment 10: In line 265, 'the CSI estimation using LSE and both-sides retrodirective system boasts the least convergence time needed to achieve the maximum possible WPT efficiency, but their implementation is more complex compared to the iterative methods.' Why is the implementation of CSI estimation using LSE and the both-sides retrodirective system more complex? This should be further elaborated.

Response 10: Thank you for this comment. The CSI estimation method requires a stronger digital signal processing capability compared to the iterative techniques while the both-sides retrodirective system requires additional analog circuitry and must operate in the marginally stable region which can be difficult to implement. More discussion has been added to address this.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thanks for your improvement of your paper. I think the majority of the reply is fine.

I have only minor comments.

1) When you mention the simulation time of each method, you need to give your computer configuration. for example, which CPU, GPU used? Memory?

2) You mention your antenna array work in the Fresnel zone. You still need to ensure they are not in the reactive near field. Please provide the reactive near field distance of your antenna.

Author Response

Dear Reviewer,

I appreciate the time and effort that you have dedicated to provide feedback on my manuscript entitled “Overview and Comparison of Feedback-based Dynamic Beam Focusing Techniques for Long-Ranged Wireless Power Transfer". I have carefully incorporated all comments in this revision. The detailed responses to each of the comments can be found after this cover statement.

Sincerely,
Charleston Dale M. Ambatali

------------------------------------------------------

Comments 1: When you mention the simulation time of each method, you need to give your computer configuration. for example, which CPU, GPU used? Memory?

Response 1: Thank you for this inquiry. I have included the computer configuration details in Section 4.2.

Comments 2: You mention your antenna array work in the Fresnel zone. You still need to ensure they are not in the reactive near field. Please provide the reactive near field distance of your antenna.

Response 1: Thank you for this comment. I confirmed that each of the simulation setups are all in the radiative near-field zone. I also provided more discussion on this in Section 4.1 and the respective discussion of the simulation setups in Section 4.2.

Reviewer 2 Report

Comments and Suggestions for Authors

It is not perfect but I recommend for publication. This is a review paper, and it has useful information.

Author Response

Dear Reviewer,

Sincerely,
Charleston Dale M. Ambatali

Reviewer 3 Report

Comments and Suggestions for Authors

n/a

Author Response

Dear Reviewer,

Sincerely,
Charleston Dale M. Ambatali

Reviewer 4 Report

Comments and Suggestions for Authors

No further comments.

Author Response

Dear Reviewer,

Sincerely,
Charleston Dale M. Ambatali

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